20,000 leagues under the sea

A submarine is exploring a part of the ocean where fresh water issues into the salty water of the ocean from both rivers and underwater springs. Preliminary measurements of the water density at different depths are given in the table below.

Depth [m]

0

50

100

200

300

400

500

600

700

ρ [kg/m3]

1000

1060

1110

1160

1190

1200

1200

1180

1160

The submarine has a volume of 100 m3 and a weight of 500 kN.
a) Determine the vertical thrust (force) that the submarine’s engines must produce in order for it to remain motionless at a depth of 650 m.
b) Assuming that the air pressure inside the submarine is standard atmospheric, determine the force on a circular glass window with a diameter of 0.20 m at the depth of 650 m. Then, compare this force with the force that would be exerted on the same window, if this submarine were submerged 650 m below the surface of lake Ontario, assumed to contain fresh water.

Contributed by Stavros Tavoularis, Department of Mechanical Engineering, University of Ottawa, Ottawa, Canada.

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